2 In a fairground game a competitor scores \(0,1,2\) or 3 with probabilities given in the following table, where \(a\) and \(b\) are constants.
| Score | 0 | 1 | 2 | 3 |
| Probability | \(a\) | \(b\) | \(b\) | \(b\) |
The competitor's expected score is 0.9 .
- Show that \(b = 0.15\).
- Find the variance of the score.
- The competitor has to pay \(\pounds 2.50\) to take part, and wins a prize of \(\pounds 2 X\), where \(X\) is the score achieved. Find the expectation of the competitor's loss.